Felurian is a faerie from the fae, who is known for taking the form of a beautiful naked human woman, luring men into the fae, and making love to them until their body or their mind is broken.
Kvothe is lured into her world, but after she teaches him much about making love, he blackmails her into letting him go, by singing a beautiful song of her but leaving it unfinished, needing the comparison of another woman in bed to complete it. Thus, they make a deal that after Kvothe has experienced the many facets of lovemaking, to return to Felurian with the completed song. She makes him a shaed, a magical protective cloak made from strands of moonlight and shadow, to protect him upon returning to the mortal world, and teaches him much about the fae and the faerie world.
Kvothe's time with Felurian seems to be around a year, but when he returns to the human world, he has been gone only 3 days.